


In which Merlin fails at explaining whether i is positive or negative

by Ren



Category: Merlin (BBC)
Genre: Alternate Universe - Modern Setting, Gen
Language: English
Status: Completed
Published: 2010-10-15
Updated: 2010-10-15
Packaged: 2017-10-12 16:55:51
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 385
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/127027
Author URL: https://archiveofourown.org/users/Ren/pseuds/Ren
Summary: <blockquote class="userstuff">
              <p>Modern AU. Merlin is a maths geek and tutors Arthur.</p>
            </blockquote>





	In which Merlin fails at explaining whether i is positive or negative

**Author's Note:**

> Drabble written for a commentfic meme. Unbetaed.

Merlin bit his pencil and fought the urge to stab Arthur with it. "Because," he said for what was probably the hundredth time that afternoon, "we're working with _imaginary numbers_."

"It makes no sense to me," Arthur repeated stubbornly. Merlin refrained from commenting on that. "If one is twice as much as the other..."

"That's not how it works," Merlin insisted. "You're used to think about real numbers, but these are imaginary numbers."

Arthur snorted. "Imaginary," he repeated, shaking his head. Merlin didn't rise to the bait. They'd already gone over just how funny the name 'imaginary numbers' was. (Very funny for Arthur. Not quite so much for Merlin.)

"You can't turn **_C_** into an ordered field," Merlin said with a sigh. "It can be partially ordered, but you can't use the same order you put on **_R_**."

In retrospect this might have not been a good choice of words since Arthur just stared at him blankly as if he'd started to speak in Chinese. It wasn't easy to explain things in Arthur-speak. "In other words, er..."

It was always like that, with Arthur. Merlin would start off trying to explain something that was very simple and end up being more confused that he started with.

"So we have _i_ and _2i_ ," Merlin tried again, pointing at the notepad in front of them. "But you can't say that one is bigger than the other."

"Why?" Arthur insisted. "One is twice as much as the other, it stands to reason!"

Merlin tapped his fingers irritably, then he had a sudden inspiration. "It's like with negative numbers," he said. "You can't say that _-2_ is bigger than _-1_ , even though it's twice as much."

He looked at Arthur expectantly. Arthur looked thoughtful for a moment, then he nodded.

"So imaginary numbers are negative," he said.

"No!" Merlin exclaimed. Arthur stared at him, as if Merlin had been the one who had made numbers so complicated. Possibly out of spite.

"What's the point of imaginary numbers, anyway?" he asked with all the certainty of a law student who only needed this one exam to get all his necessary maths credits.

Merlin rolled his eyes and gave up. "None at all, they just exist to aggravate you. Just trust me on this, _i_ is not positive. Or negative. Okay?"


End file.
